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An improved CMA for dispersion compensation in 100 Gbps DP-QPSK optical signal transmission system
Optik 136 (2017) 480–486
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
An improved CMA for dispersion compensation in 100 Gbps DP-QPSK optical signal transmission system Jiangyi Qin, Chunwu Liu, Zhiping Huang ∗ , Shaojing Su, Yimeng Zhang College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha 410073, Hunan Province, PR China
a r t i c l e
i n f o
Article history: Received 2 February 2014 Received in revised form 29 April 2014 Accepted 11 February 2017 Keywords: Optical communications Constant modulus algorithm Dispersion compensation Variable step size Mean-square error
a b s t r a c t An improved constant modulus algorithm (CMA) for dispersion compensation in 100 Gbps Dual Polarization-Quadrature Phase Shift Keying (DP-QPSK) optical signal transmission system is proposed to achieve better reliability receiving performances. In the receiver, we combine variable step size and Mean-Square Error (MSE) to improve the conventional CMA. Compared to conventional CMA, the proposed algorithm has a better performance in adapting the time varying channel and the strong noise. Meanwhile, the proposed algorithm has a faster convergence rate than the previous one. Simulation results show that the improved CMA can achieve the dispersion and polarization demultiplexing of 100 Gbps DP-QPSK optical signal transmission system efficiently. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction With the rapid development of optical fiber communication technology, high speed rate as well as large capacity has become the development tendency of modern fiber transmission system. Besides using the dense wavelength division multiplexing (DWDM) technology and reducing the channel spacing, improving the speed of each single wave is one solution to enlarge the capacity of optical networks. Nowadays, 100 Gbps DP-QPSK optical signal transmission system based on coherent detection and digital signal processing (DSP) technology has been developed and will be applied to the optical backbone networks in the future [1–4]. DP-QPSK is based on two polarization modes (horizontal electric mode and the transverse magnetic mode). Using polarization multiplexing technology, on the premise of small price, DP-QPSK can double spectrum efficiency directly and make the system of symbol rate reduced to half of their original cost at the same time. Therefore, DP-QPSK signal information rate is four times of that of the baud rate. Under the same bit rate, DP-QPSK system capacity is four times that of Differential Phase Shift Keying (DPSK) and Differential Quarter Phase Shift Keying (DQPSK) is twice as much [5–8]. However, to the 100Gbps high speed and long distance optical signal transmission system, it has much lower dispersion tolerance than low speed systems. For this reason, it is difficult and necessary to resolve the dispersion effect in 100 Gbps DP-QPSK optical signal transmission system. In this paper we propose an improved CMA for 100 Gbps DP-QPSK optical signal transmission system. On the one hand, the conventional CMA has slow convergence rate. In the conventional CMA, a fixed step size is used to update the coefficients of equalization. However, the fixed step size cannot achieve fast convergence rate and low residual error simultaneously. Therefore, in the improved CMA that we propose, variable step size is used to improve the calculating efficiency of the compensation algorithm [9–11]. On the other hand,
∗ Corresponding author. E-mail address: [email protected] (Z. Huang). http://dx.doi.org/10.1016/j.ijleo.2017.02.040 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
J. Qin et al. / Optik 136 (2017) 480–486
481
the performance of the conventional CMA is easily affected by interference signal. In the conventional CMA, we use residual error to control the update of the equalization’s coefficients. Because optical fiber channel is time varying, so the residual error will augment by channel interference signal. For this reason, we choose MSE to replace residual error as the control variable of the improved CMA [12–15]. In addition, the modulation format of DP-QPSK leads to polarization crosstalk which will impact the transmission system seriously. The improved CMA can resolve the problem simultaneously. The rest of paper is organized as follow: Section 2 describes the improved CMA for dispersion compensation in detail. Section 3 outlines the 100 Gbps DP-QPSK optical signal transmission simulation system, in which the improved CMA we proposed is employed. In Section 4, simulation results and relevant discussions are described, and finally, Section 5 concludes the paper. 2. Improved CMA 2.1. Channel impairments In the 100 Gbps DP-QPSK optical signal transmission system, attenuation, dispersion and nonlinear effect are the main channel impairment. In this paper, we will discuss the dispersion and polarization crosstalk in detail [16–18]. Dispersion includes chromatic dispersion (CD) and polarization mode dispersion (PMD). Dispersion impairment function in frequency domain is given by:
U=
u1 (w)
u2 (w)
−u2 ∗ (w)
u1 ∗ (w)
H(w) =
u1 (w)
u2 (w)
−u2 ∗ (w)
u1 ∗ (w)
(1)
× exp(−j
S2 z 2 w ) 4c
(2)
Where U is the jones matrix, S is chromatic dispersion, is the wavelength of optical signal, z is the distance of propagation, w is the frequency of dispersion impairment function and c is the speed of light. The constellation diagram of DP-QPSK is shown in Fig. 1.In order to simplify the derivation, we use phase information to express DP-QPSK optical signal. If the transmitted DP-QPSK optical signal is given by (EV , EH ) = (ejϕV (t) , ejϕH (t) ), the impaired DP-QPSK optical signal can be expressed as follow:
ejϕX (t) ejϕY (t)
=
h11 ejϕV (t) + h12 ejϕH (t)
(3)
h21 ejϕV (t) + h22 ejϕH (t)
Where hij is the impulse response which is caused by i polarization signal and affect j polarization signal. 2.2. Conventional CMA From (3) we can see that the two impaired polarization signal contain all polarization information of transmitting terminal. Therefore, we need a butterfly equalization which is including four Finite Impulse Response (FIR) filters to compensate dispersion and resolve polarization crosstalk. Firstly, we should use a fixed coefficients filter to compensate large amounts of chromatic dispersion which is caused by the fiber channel. Then, butterfly equalization is used to compensate the residual dispersion and resolve the polarization crosstalk. The digital signal processing which is including CMA is shown in Fig. 2. In order to realize dispersion compensation and polarization demultiplexing, it is important to utilize some algorithms to adjust the coefficientsof butterfly equalization. In DP-QPSK system with optical coherent receiver, we adopt CMA to adjust the Hxx , Hxy , Hyy , Hyx usually.
Fig. 1. constellation diagram of DP-QPSK.
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Fig. 2. digital signal processing module.
Fig. 3. 100Gbps DP-QPSK optical signal transmission simulation model.
The coefficients iteration equations of conventional CMA can be expressed as follow:
Hxx = Hxx + εx X × X ∗
Hxy = Hxy + εy X × Y ∗
Hyx = Hyx + εy Y × X ∗
(4)
Hyy = Hyy + εy Y × Y ∗ Where is step, εx is the error function of X polarization signal, εy is the error function of Y polarization signal. Because the modulation amplitude of DP-QPSK optical signal is constant, the error function can be expressed as follow:
2
2
εx = 1 − |X |
εy = 1 − |Y |
(5)
When the error functions tend to zero, the processing of dispersion compensation and polarization demultiplexing is completed. From the paper we can see that CMA only pays attention to the amplitude information. Therefore, even if the optical signal has phase impairment, we can also use CMA to solve the problems. 2.3. Improved CMA In order to enhance the convergence rate and performance of conventional CMA, we use variable step size to replace the fixed one firstly. At the beginning of CMA, the variable step size is a big one which can accelerate the convergence rate.
J. Qin et al. / Optik 136 (2017) 480–486
constellation diagram after compensation -X
2
2
1
1
Quadrature
Quadrature
constellation diagram before compensation -X
0 -1 -2
0 -1 -2
-2
-1
0 In-Phase
1
2
-2
constellation diagram before compensation -Y
-1
0 In-Phase
1
2
constellation diagram after compensation -Y
2
2
1
1
Quadrature
Quadrature
483
0 -1 -2
0 -1 -2
-2
-1
0 In-Phase
1
2
-2
-1
0 In-Phase
1
2
Fig. 4. conventional CMA simulation result.
As the error function tends to zero, the step size is decreasing. In this way, improved CMA has a smaller residue error. The variable step size can be expressed as follow: (n + 1) = ˛(n) + ˇε
(5)
Where (n) is the variable step, ␣ and ˇ are the step size control factors, ε is the error function. In the conventional CMA, we use residual error to control coefficients iteration. However, this method exist some shortcomings. Especially, channel interference signal has a significant impact on residual error. When there is a strong interference signal in optical fiber, the residual error will be amplified suddenly. As a result, the step size will become larger, and the convergence performance will become worse. In order to solve this problem, we use MSE to replace the residual error. In the practical application, the residual error should be taken square and pass the shifting rectangular window whose length is M. At last, we can get the MSE by averaging the result coming from the rectangular window. Through windowing and averaging, MSE can reduce the impact which is caused by channel interference signal. The length of rectangular window is a significant factor in convergence rate and convergence performance of the improved CMA. If M is a smaller value, the improved CMA would have a stronger adaptability to the time-varying channel. However, it would have a slower convergence rate. Therefore, we should choose an appropriate value for different situations. The detailed steps of improved CMA are described as follow:
(1) Initialize the starting coefficients of CMA as Hxx = · · · 0
1
0 · · · , Hxy = · · · 0
0
0 · · · , Hyx = · · · 0
0
0 · · · , and
Hyy = · · · 0 1 0 · · · . (2) Run CMA for butterfly equalizer and the iteration times are M. (3) Calculate MSE and shift the rectangle window. (4) If the MSE converges to certain accuracy, finish iteration. Otherwise, change the step size and return to (2).
3. Simulation model We have conducted simulations in Optisystem11.0 to setup 100 Gbps DP-QPSK optical signal transmission model. There are attenuation, dispersion and nonlinear effect in the simulation transmission channel. Then, we can get the impaired signal and unite Matlab to verify the performance of improved CMA. The simulation model is depicted in Fig. 3.
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constellation diagram after compensation -X(0.005)
2
2
1
1
Quadrature
Quadrature
constellation diagram after compensation -X(0.0005)
0 -1 -2
-1 -2
-2
-1
0 In-Phase
1
2
-2
constellation diagram after compensation -Y(0.0005) 2
2
1
1
0 -1 -2
-1
0 In-Phase
1
2
constellation diagram after compensation -Y(0.005) Quadrature
Quadrature
0
0 -1 -2
-2
-1
0 In-Phase
1
2
-2
-1
0 In-Phase
1
2
Fig. 5. conventional CMA simulation result of different step sizes.
In this simulation model, 100 Gbps DP-QPSK optical signal is modulated and transmitted at the transmit module. The transmission distance is 500 km, and the optical signal is impaired by dispersion and nonlinear effect in the transmission channel. In the receiver, 100 Gbps DP-QPSK optical signal is demodulated and sampled by ADCs. After that, the optical signal has become four digital signals. In the DSP unit, four digital signals are processed by timing recovery, dispersion compensation, polarization demultiplexing, frequency estimation, carrier phase estimation and symbol estimation and decoding. The DSP code is changed by Matlab to produce different simulation results. In this paper, we just verify dispersion compensation algorithm. 4. Simulation results Firstly, in the 100 Gbps DP-QPSK optical signal transmission simulation model, we use conventional CMA to compensate dispersion effect and resolve polarization crosstalk. The number of tap is 33, both of the step size control factors are 0.01, length of the rectangle window is 4000, and the fixed step size is 0.001. The simulation result is shown in Fig. 4. From the conventional CMA simulation result, we can see that the sampled data have gathered together and formed four constellation diagrams after compensation. However, the constellation diagrams are too dispersed. It means that the convergence performance is not perfect. Therefore, conventional CMA cannot compensate the impaired 100 Gbps DP-QPSK optical signal admirably. In order to research the relation between step size and convergence performance, we use other step size to simulate. The simulation results are shown in Fig. 5. From Fig. 5, we can see that the step size is of great importance to the convergence performance. When the step size become larger (0.005), the convergence performance becomes worse. The larger step size will lead to larger residual error and make constellation diagrams more dispersed. When the step size become smaller (0.0005), the convergence performance is not good enough either. Because the smaller step size will lead to slower convergence rate. The constellation diagrams cannot be convergent enough in the certain iteration times. Therefore, we use improved CMA to process the impaired data, the simulation results are shown in Fig. 6. In this simulation, the number of tap is 33, both of the step size control factors are 0.01, length of the rectangle window is 4000, and the initial step size is 0.005. After iteration, the final step size is 0.0024. From the improved CMA simulation result, we can see that the improved CMA has a better convergence performance than the conventional CMA. And the constellation diagrams can be convergent good enough for following processing.
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Fig. 6. improved CMA simulation result.
0.5 0.005 0.0005 0.001 variable step
0.45 0.4
MSE value
0.35 0.3 0.25 0.2 0.15 0.1
1
2
3
4
5 6 7 iteration times/4000
8
9
10
11
Fig. 7. the convergence curve of improved CMA.
Meanwhile, the convergence curve is given in Fig. 7.From the convergence curve of improved CMA, we can see that the improved CMA has a faster convergence rate than the conventional CMA. It can use less iteration times to meet certain accuracy.
5. Conclusion In this paper, we developed an improved CMA for dispersion compensation in 100 Gbps DP-QPSK optical signal transmission system. We compared the performances between the proposed algorithm and previous one. Then, we use Optisystem11.0 to set up a simulation model of 100 Gbps DP-QPSK optical signal transmission system. Simulation results showed that the proposed algorithm has a better convergence performance and convergence rate.
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References [1] Jing Zhou, Zhiping Huang, Chunwu Liu, Shaojing Su, Design of adaptive dispersion compensation and demodulation system for 40 Gbps RZ-DQPSK optical fiber communication receivers, Optik 125 (2014) 370–373. [2] B. Kantarci, H. Mouftah, Bandwidth distribution solutions for performance enhancement in long-reach passive optical networks, IEEE Commun. Surv. Tutorials 99 (2011) 1–20. [3] A. Mukherjee, S.P. Singh, V.K. Chaubey, Wavelength conversion algorithm in an intelligent WDM network, Opt. Commun. 230 (2004) 59–65. [4] M. Kuschnerov, F.N. Hauske, K. Piyawanno, B. Spinnler, M.S. Alfiad, A. Napoli, B. Lankl, DSP for coherent single-carrier receivers, J. Lightwave Technol. 27 (2009) 3614–3622. [5] Xiaobo Meng, Weiqin Zhou, Chao Ge, Xian Zhou, Xue Chen, Long-haul 112 Gbit/s coherent polarization multiplexing QPSK transmission experiment on G.652 fiber with the improved DSP unit, Optik 124 (2013) 3665–3670. [6] T.J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, C. Urricariet, End-to-end native IP data 100 G single carrier real time DSP coherent detection transport over 1520-km field deployed fiber, OFC/NFOEC PDPD4 (2010). [7] X. Meng, Y. Liu, Y. Shi, X. Chen, C. Ge, W. Zhou, 112 Gbit/s long-reach real-time coherent passive optical network downlink transmission experiment based on polarization multiplexing quadrature phase shift keying format, Opt. Eng. 51 (2012) 211. [8] Vinita Tiwari, Debabrata Sikdar, M. Navya Jyothi, Gauri Dixit, V.K. Chaubey, Investigation of optimum pulse shape for 112 Gbps DP-DQPSK in DWDM transmission, Optik 124 (2013) 5567–5572. [9] Hong Chae Woo, Variable step size LMS algorithm using squared error and autocorrelation of error, Procedia Eng. 41 (2012) 41–52. [10] Ying Liu, Raghuram Ranganathan, Matthew T. Hunter, Wasfy B. Mikhael, Complex adaptive LMS algorithm employing the conjugate Gradient principle for channel estimation and equalization, Circuits Syst. Signal Process. 31 (3) (2012) 1067–1087. [11] M.B. Suleiman, H. Musa, F. Ismail, N. Senu, A new variable step size block backward differentiation formula for solving stiff initial value problems, Int. J. Comput. Math. 90 (11) (2013) 2391–2408. [12] Lingfeng Yu, Lilong Cai, Data encrypti on by disarranging the holographic information with rotated holograms, Optik 114 (11) (2003) 497–503. [13] Chih-Chun Feng, Chong-Yung Chi, Design of Wiener filters using a cumulant based MSE criterion, Signal Process. 54 (1) (1996) 23–48. [14] Monika Pinchas, A novel expression for the achievable MSE performance obtained by blind adaptive equalizers, Signal Image Video Process. 7 (1) (2013) 67–74. [15] R. Johnson Jr., P. Schniter, T.J. Endres, J.D. Behm, D.R. Brown, R.A. Casas, Blind equalization using the constant modulus criterion: a review, Proc. IEEE 86 (1998) 1927–1950. [16] Diego E. Crivelli Hugo, S. Carrer Mario, R. Hueda, Adaptive digital equalization in the presence of chromatic dispersion, PMD, and phase noise in coherent fiber optic systems, IEEE Commun. Soc. Globecom (2004) 2545–2551. [17] X. Zhou, X. Chen, W. Zhou, Y. Fan, H. Zhu, Z. Li, All-digital timing recovery and adaptive equalization for 112Gbit/s POLMUX-NRZ-DQPSK optical coherent receivers, J. Opt. Commun. Netw. 2 (2010) 984–990. [18] A. Orlandini, L. Vincetti, A simple and useful model for Jones matrix to evaluate higher order polarization-mode dispersion effects, IEEE Photon. Technol. Lett. 13 (2001) 1176–1178.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Original research article
An improved CMA for dispersion compensation in 100 Gbps DP-QPSK optical signal transmission system Jiangyi Qin, Chunwu Liu, Zhiping Huang ∗ , Shaojing Su, Yimeng Zhang College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha 410073, Hunan Province, PR China
a r t i c l e
i n f o
Article history: Received 2 February 2014 Received in revised form 29 April 2014 Accepted 11 February 2017 Keywords: Optical communications Constant modulus algorithm Dispersion compensation Variable step size Mean-square error
a b s t r a c t An improved constant modulus algorithm (CMA) for dispersion compensation in 100 Gbps Dual Polarization-Quadrature Phase Shift Keying (DP-QPSK) optical signal transmission system is proposed to achieve better reliability receiving performances. In the receiver, we combine variable step size and Mean-Square Error (MSE) to improve the conventional CMA. Compared to conventional CMA, the proposed algorithm has a better performance in adapting the time varying channel and the strong noise. Meanwhile, the proposed algorithm has a faster convergence rate than the previous one. Simulation results show that the improved CMA can achieve the dispersion and polarization demultiplexing of 100 Gbps DP-QPSK optical signal transmission system efficiently. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction With the rapid development of optical fiber communication technology, high speed rate as well as large capacity has become the development tendency of modern fiber transmission system. Besides using the dense wavelength division multiplexing (DWDM) technology and reducing the channel spacing, improving the speed of each single wave is one solution to enlarge the capacity of optical networks. Nowadays, 100 Gbps DP-QPSK optical signal transmission system based on coherent detection and digital signal processing (DSP) technology has been developed and will be applied to the optical backbone networks in the future [1–4]. DP-QPSK is based on two polarization modes (horizontal electric mode and the transverse magnetic mode). Using polarization multiplexing technology, on the premise of small price, DP-QPSK can double spectrum efficiency directly and make the system of symbol rate reduced to half of their original cost at the same time. Therefore, DP-QPSK signal information rate is four times of that of the baud rate. Under the same bit rate, DP-QPSK system capacity is four times that of Differential Phase Shift Keying (DPSK) and Differential Quarter Phase Shift Keying (DQPSK) is twice as much [5–8]. However, to the 100Gbps high speed and long distance optical signal transmission system, it has much lower dispersion tolerance than low speed systems. For this reason, it is difficult and necessary to resolve the dispersion effect in 100 Gbps DP-QPSK optical signal transmission system. In this paper we propose an improved CMA for 100 Gbps DP-QPSK optical signal transmission system. On the one hand, the conventional CMA has slow convergence rate. In the conventional CMA, a fixed step size is used to update the coefficients of equalization. However, the fixed step size cannot achieve fast convergence rate and low residual error simultaneously. Therefore, in the improved CMA that we propose, variable step size is used to improve the calculating efficiency of the compensation algorithm [9–11]. On the other hand,
∗ Corresponding author. E-mail address: [email protected] (Z. Huang). http://dx.doi.org/10.1016/j.ijleo.2017.02.040 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
J. Qin et al. / Optik 136 (2017) 480–486
481
the performance of the conventional CMA is easily affected by interference signal. In the conventional CMA, we use residual error to control the update of the equalization’s coefficients. Because optical fiber channel is time varying, so the residual error will augment by channel interference signal. For this reason, we choose MSE to replace residual error as the control variable of the improved CMA [12–15]. In addition, the modulation format of DP-QPSK leads to polarization crosstalk which will impact the transmission system seriously. The improved CMA can resolve the problem simultaneously. The rest of paper is organized as follow: Section 2 describes the improved CMA for dispersion compensation in detail. Section 3 outlines the 100 Gbps DP-QPSK optical signal transmission simulation system, in which the improved CMA we proposed is employed. In Section 4, simulation results and relevant discussions are described, and finally, Section 5 concludes the paper. 2. Improved CMA 2.1. Channel impairments In the 100 Gbps DP-QPSK optical signal transmission system, attenuation, dispersion and nonlinear effect are the main channel impairment. In this paper, we will discuss the dispersion and polarization crosstalk in detail [16–18]. Dispersion includes chromatic dispersion (CD) and polarization mode dispersion (PMD). Dispersion impairment function in frequency domain is given by:
U=
u1 (w)
u2 (w)
−u2 ∗ (w)
u1 ∗ (w)
H(w) =
u1 (w)
u2 (w)
−u2 ∗ (w)
u1 ∗ (w)
(1)
× exp(−j
S2 z 2 w ) 4c
(2)
Where U is the jones matrix, S is chromatic dispersion, is the wavelength of optical signal, z is the distance of propagation, w is the frequency of dispersion impairment function and c is the speed of light. The constellation diagram of DP-QPSK is shown in Fig. 1.In order to simplify the derivation, we use phase information to express DP-QPSK optical signal. If the transmitted DP-QPSK optical signal is given by (EV , EH ) = (ejϕV (t) , ejϕH (t) ), the impaired DP-QPSK optical signal can be expressed as follow:
ejϕX (t) ejϕY (t)
=
h11 ejϕV (t) + h12 ejϕH (t)
(3)
h21 ejϕV (t) + h22 ejϕH (t)
Where hij is the impulse response which is caused by i polarization signal and affect j polarization signal. 2.2. Conventional CMA From (3) we can see that the two impaired polarization signal contain all polarization information of transmitting terminal. Therefore, we need a butterfly equalization which is including four Finite Impulse Response (FIR) filters to compensate dispersion and resolve polarization crosstalk. Firstly, we should use a fixed coefficients filter to compensate large amounts of chromatic dispersion which is caused by the fiber channel. Then, butterfly equalization is used to compensate the residual dispersion and resolve the polarization crosstalk. The digital signal processing which is including CMA is shown in Fig. 2. In order to realize dispersion compensation and polarization demultiplexing, it is important to utilize some algorithms to adjust the coefficientsof butterfly equalization. In DP-QPSK system with optical coherent receiver, we adopt CMA to adjust the Hxx , Hxy , Hyy , Hyx usually.
Fig. 1. constellation diagram of DP-QPSK.
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Fig. 2. digital signal processing module.
Fig. 3. 100Gbps DP-QPSK optical signal transmission simulation model.
The coefficients iteration equations of conventional CMA can be expressed as follow:
Hxx = Hxx + εx X × X ∗
Hxy = Hxy + εy X × Y ∗
Hyx = Hyx + εy Y × X ∗
(4)
Hyy = Hyy + εy Y × Y ∗ Where is step, εx is the error function of X polarization signal, εy is the error function of Y polarization signal. Because the modulation amplitude of DP-QPSK optical signal is constant, the error function can be expressed as follow:
2
2
εx = 1 − |X |
εy = 1 − |Y |
(5)
When the error functions tend to zero, the processing of dispersion compensation and polarization demultiplexing is completed. From the paper we can see that CMA only pays attention to the amplitude information. Therefore, even if the optical signal has phase impairment, we can also use CMA to solve the problems. 2.3. Improved CMA In order to enhance the convergence rate and performance of conventional CMA, we use variable step size to replace the fixed one firstly. At the beginning of CMA, the variable step size is a big one which can accelerate the convergence rate.
J. Qin et al. / Optik 136 (2017) 480–486
constellation diagram after compensation -X
2
2
1
1
Quadrature
Quadrature
constellation diagram before compensation -X
0 -1 -2
0 -1 -2
-2
-1
0 In-Phase
1
2
-2
constellation diagram before compensation -Y
-1
0 In-Phase
1
2
constellation diagram after compensation -Y
2
2
1
1
Quadrature
Quadrature
483
0 -1 -2
0 -1 -2
-2
-1
0 In-Phase
1
2
-2
-1
0 In-Phase
1
2
Fig. 4. conventional CMA simulation result.
As the error function tends to zero, the step size is decreasing. In this way, improved CMA has a smaller residue error. The variable step size can be expressed as follow: (n + 1) = ˛(n) + ˇε
(5)
Where (n) is the variable step, ␣ and ˇ are the step size control factors, ε is the error function. In the conventional CMA, we use residual error to control coefficients iteration. However, this method exist some shortcomings. Especially, channel interference signal has a significant impact on residual error. When there is a strong interference signal in optical fiber, the residual error will be amplified suddenly. As a result, the step size will become larger, and the convergence performance will become worse. In order to solve this problem, we use MSE to replace the residual error. In the practical application, the residual error should be taken square and pass the shifting rectangular window whose length is M. At last, we can get the MSE by averaging the result coming from the rectangular window. Through windowing and averaging, MSE can reduce the impact which is caused by channel interference signal. The length of rectangular window is a significant factor in convergence rate and convergence performance of the improved CMA. If M is a smaller value, the improved CMA would have a stronger adaptability to the time-varying channel. However, it would have a slower convergence rate. Therefore, we should choose an appropriate value for different situations. The detailed steps of improved CMA are described as follow:
(1) Initialize the starting coefficients of CMA as Hxx = · · · 0
1
0 · · · , Hxy = · · · 0
0
0 · · · , Hyx = · · · 0
0
0 · · · , and
Hyy = · · · 0 1 0 · · · . (2) Run CMA for butterfly equalizer and the iteration times are M. (3) Calculate MSE and shift the rectangle window. (4) If the MSE converges to certain accuracy, finish iteration. Otherwise, change the step size and return to (2).
3. Simulation model We have conducted simulations in Optisystem11.0 to setup 100 Gbps DP-QPSK optical signal transmission model. There are attenuation, dispersion and nonlinear effect in the simulation transmission channel. Then, we can get the impaired signal and unite Matlab to verify the performance of improved CMA. The simulation model is depicted in Fig. 3.
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constellation diagram after compensation -X(0.005)
2
2
1
1
Quadrature
Quadrature
constellation diagram after compensation -X(0.0005)
0 -1 -2
-1 -2
-2
-1
0 In-Phase
1
2
-2
constellation diagram after compensation -Y(0.0005) 2
2
1
1
0 -1 -2
-1
0 In-Phase
1
2
constellation diagram after compensation -Y(0.005) Quadrature
Quadrature
0
0 -1 -2
-2
-1
0 In-Phase
1
2
-2
-1
0 In-Phase
1
2
Fig. 5. conventional CMA simulation result of different step sizes.
In this simulation model, 100 Gbps DP-QPSK optical signal is modulated and transmitted at the transmit module. The transmission distance is 500 km, and the optical signal is impaired by dispersion and nonlinear effect in the transmission channel. In the receiver, 100 Gbps DP-QPSK optical signal is demodulated and sampled by ADCs. After that, the optical signal has become four digital signals. In the DSP unit, four digital signals are processed by timing recovery, dispersion compensation, polarization demultiplexing, frequency estimation, carrier phase estimation and symbol estimation and decoding. The DSP code is changed by Matlab to produce different simulation results. In this paper, we just verify dispersion compensation algorithm. 4. Simulation results Firstly, in the 100 Gbps DP-QPSK optical signal transmission simulation model, we use conventional CMA to compensate dispersion effect and resolve polarization crosstalk. The number of tap is 33, both of the step size control factors are 0.01, length of the rectangle window is 4000, and the fixed step size is 0.001. The simulation result is shown in Fig. 4. From the conventional CMA simulation result, we can see that the sampled data have gathered together and formed four constellation diagrams after compensation. However, the constellation diagrams are too dispersed. It means that the convergence performance is not perfect. Therefore, conventional CMA cannot compensate the impaired 100 Gbps DP-QPSK optical signal admirably. In order to research the relation between step size and convergence performance, we use other step size to simulate. The simulation results are shown in Fig. 5. From Fig. 5, we can see that the step size is of great importance to the convergence performance. When the step size become larger (0.005), the convergence performance becomes worse. The larger step size will lead to larger residual error and make constellation diagrams more dispersed. When the step size become smaller (0.0005), the convergence performance is not good enough either. Because the smaller step size will lead to slower convergence rate. The constellation diagrams cannot be convergent enough in the certain iteration times. Therefore, we use improved CMA to process the impaired data, the simulation results are shown in Fig. 6. In this simulation, the number of tap is 33, both of the step size control factors are 0.01, length of the rectangle window is 4000, and the initial step size is 0.005. After iteration, the final step size is 0.0024. From the improved CMA simulation result, we can see that the improved CMA has a better convergence performance than the conventional CMA. And the constellation diagrams can be convergent good enough for following processing.
J. Qin et al. / Optik 136 (2017) 480–486
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Fig. 6. improved CMA simulation result.
0.5 0.005 0.0005 0.001 variable step
0.45 0.4
MSE value
0.35 0.3 0.25 0.2 0.15 0.1
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4
5 6 7 iteration times/4000
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Fig. 7. the convergence curve of improved CMA.
Meanwhile, the convergence curve is given in Fig. 7.From the convergence curve of improved CMA, we can see that the improved CMA has a faster convergence rate than the conventional CMA. It can use less iteration times to meet certain accuracy.
5. Conclusion In this paper, we developed an improved CMA for dispersion compensation in 100 Gbps DP-QPSK optical signal transmission system. We compared the performances between the proposed algorithm and previous one. Then, we use Optisystem11.0 to set up a simulation model of 100 Gbps DP-QPSK optical signal transmission system. Simulation results showed that the proposed algorithm has a better convergence performance and convergence rate.
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References [1] Jing Zhou, Zhiping Huang, Chunwu Liu, Shaojing Su, Design of adaptive dispersion compensation and demodulation system for 40 Gbps RZ-DQPSK optical fiber communication receivers, Optik 125 (2014) 370–373. [2] B. Kantarci, H. Mouftah, Bandwidth distribution solutions for performance enhancement in long-reach passive optical networks, IEEE Commun. Surv. Tutorials 99 (2011) 1–20. [3] A. Mukherjee, S.P. Singh, V.K. Chaubey, Wavelength conversion algorithm in an intelligent WDM network, Opt. Commun. 230 (2004) 59–65. [4] M. Kuschnerov, F.N. Hauske, K. Piyawanno, B. Spinnler, M.S. Alfiad, A. Napoli, B. Lankl, DSP for coherent single-carrier receivers, J. Lightwave Technol. 27 (2009) 3614–3622. [5] Xiaobo Meng, Weiqin Zhou, Chao Ge, Xian Zhou, Xue Chen, Long-haul 112 Gbit/s coherent polarization multiplexing QPSK transmission experiment on G.652 fiber with the improved DSP unit, Optik 124 (2013) 3665–3670. [6] T.J. Xia, G. Wellbrock, B. Basch, S. Kotrla, W. Lee, T. Tajima, K. Fukuchi, M. Cvijetic, J. Sugg, Y. Ma, B. Turner, C. Cole, C. Urricariet, End-to-end native IP data 100 G single carrier real time DSP coherent detection transport over 1520-km field deployed fiber, OFC/NFOEC PDPD4 (2010). [7] X. Meng, Y. Liu, Y. Shi, X. Chen, C. Ge, W. Zhou, 112 Gbit/s long-reach real-time coherent passive optical network downlink transmission experiment based on polarization multiplexing quadrature phase shift keying format, Opt. Eng. 51 (2012) 211. [8] Vinita Tiwari, Debabrata Sikdar, M. Navya Jyothi, Gauri Dixit, V.K. Chaubey, Investigation of optimum pulse shape for 112 Gbps DP-DQPSK in DWDM transmission, Optik 124 (2013) 5567–5572. [9] Hong Chae Woo, Variable step size LMS algorithm using squared error and autocorrelation of error, Procedia Eng. 41 (2012) 41–52. [10] Ying Liu, Raghuram Ranganathan, Matthew T. Hunter, Wasfy B. Mikhael, Complex adaptive LMS algorithm employing the conjugate Gradient principle for channel estimation and equalization, Circuits Syst. Signal Process. 31 (3) (2012) 1067–1087. [11] M.B. Suleiman, H. Musa, F. Ismail, N. Senu, A new variable step size block backward differentiation formula for solving stiff initial value problems, Int. J. Comput. Math. 90 (11) (2013) 2391–2408. [12] Lingfeng Yu, Lilong Cai, Data encrypti on by disarranging the holographic information with rotated holograms, Optik 114 (11) (2003) 497–503. [13] Chih-Chun Feng, Chong-Yung Chi, Design of Wiener filters using a cumulant based MSE criterion, Signal Process. 54 (1) (1996) 23–48. [14] Monika Pinchas, A novel expression for the achievable MSE performance obtained by blind adaptive equalizers, Signal Image Video Process. 7 (1) (2013) 67–74. [15] R. Johnson Jr., P. Schniter, T.J. Endres, J.D. Behm, D.R. Brown, R.A. Casas, Blind equalization using the constant modulus criterion: a review, Proc. IEEE 86 (1998) 1927–1950. [16] Diego E. Crivelli Hugo, S. Carrer Mario, R. Hueda, Adaptive digital equalization in the presence of chromatic dispersion, PMD, and phase noise in coherent fiber optic systems, IEEE Commun. Soc. Globecom (2004) 2545–2551. [17] X. Zhou, X. Chen, W. Zhou, Y. Fan, H. Zhu, Z. Li, All-digital timing recovery and adaptive equalization for 112Gbit/s POLMUX-NRZ-DQPSK optical coherent receivers, J. Opt. Commun. Netw. 2 (2010) 984–990. [18] A. Orlandini, L. Vincetti, A simple and useful model for Jones matrix to evaluate higher order polarization-mode dispersion effects, IEEE Photon. Technol. Lett. 13 (2001) 1176–1178.